Question: What do the following two equations represent? $-x+3y = -4$ $-9x-3y = 2$
Solution: Putting the first equation in $y = mx + b$ form gives: $-x+3y = -4$ $3y = x-4$ $y = \dfrac{1}{3}x - \dfrac{4}{3}$ Putting the second equation in $y = mx + b$ form gives: $-9x-3y = 2$ $-3y = 9x+2$ $y = -3x - \dfrac{2}{3}$ The slopes are negative inverses of each other, so the lines are perpendicular.